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This article is cited in 11 scientific papers (total in 12 papers)
Harmonic analysis on local fields and adelic spaces. II
D. V. Osipov, A. N. Parshin
Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
We develop harmonic analysis in certain categories of filtered Abelian
groups and vector spaces. The objects of these categories include
local fields and adelic spaces arising from arithmetic surfaces.
We prove some structure theorems for quotients of the adèle groups
of algebraic and arithmetic surfaces.
Keywords:
arithmetic surfaces, higher adèles, harmonic analysis, Fourier transform,
Poisson summation formulae.
DOI:
https://doi.org/10.4213/im4278
 Full text:
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English version:
Izvestiya: Mathematics, 2011, 75:4, 749–814
Bibliographic databases:
     
UDC:
512.75
MSC: 11R56, 18B30, 43A70
Received: 22.12.2009
Revised: 10.12.2010
Citation:
D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. RAN. Ser. Mat., 75:4 (2011), 91–164; Izv. Math., 75:4 (2011), 749–814
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/izv4278https://doi.org/10.4213/im4278 http://mi.mathnet.ru/eng/izv/v75/i4/p91
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Cycle of papers
This publication is cited in the following articles:
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A. N. Parshin, “Notes on the Poisson formula”, St. Petersburg Math. J., 23:5 (2012), 781–818
 -
Previdi L., “Locally compact objects in exact categories”, Internat. J. Math., 22:12 (2011), 1787–1821
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Osipov D.V., Parshin A.N., “Harmonic analysis and the Riemann-Roch theorem”, Dokl. Math., 84:3 (2011), 826–829
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S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197
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D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. Math., 77:4 (2013), 714–741
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A. Cámara, “Locally convex structures on higher local fields”, J. Number Theory, 143 (2014), 185–213
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Ivan Fesenko, “Geometric adeles and the Riemann–Roch theorem for $1$-cycles on surfaces”, Mosc. Math. J., 15:3 (2015), 435–453
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D. V. Osipov, A. N. Parshin, “Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields”, Proc. Steklov Inst. Math., 292 (2016), 185–201
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Liu D., “Residues and duality on semi-local two-dimensional adeles”, J. Algebra, 448 (2016), 74–83
-
Liu D., Zhu Y., “Lca(2), Weil Index, and Product Formula”, Adv. Math., 329 (2018), 1088–1136
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D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Math. J., 30 (2019), 111–122
-
D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. Math., 82:4 (2018), 817–836
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